RMSE formulaIf you fit a regression model, you can get the RMSE of the model. From our documentation, RMSE is the standard deviation of the random error. To me that would imply if you took the stdev of the residuals of the model, it would equal the RMSE, but this is not true. The values are close but not exact, see the below example (RMSE = 3.03, Stdev of Residuals = 2.99):
So I'm wondered what I'm missing here as my assumption is not correct.
Re: RMSE formulaFor the regression model, MSE = SSe/df = 348.9/38, for the sample standard deviation, SD = SSe/(n-1) = 348.9/39. In the regression model, you're losing an extra degree of freedom by estimating the slope.
Re: RMSE formulaRMSE is the square root of the MSE which is 9.182 in the ANOVA table. The DF you need in the denominator is 38.
Re: RMSE formulaIf you were just calculating the mean, the RMSE would be the SD of the residuals. But you need one DF for the model to calculate slope.
Re: RMSE formula@DonMcCormack @andreacoombs thanks, that explains it! I was confused because when I looked up the formula for RMSE, it showed a N-1 in the denominator which matches the N-1 used for the sample stdev, but apparently those N's are not the same. Once you fit a linear regression you used 2 DF's actually (1 for the mean and 1 for the slope), so the denominator for RMSE is actually N-2 in this case. Multiplying the stdev of residuals by sqrt(39/38) gives a matching result in the above example.
